Existence results for the Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds in the null case

DOI10.1007/s00220-014-2133-7zbMath1310.58025OpenAlexW2136514230WikidataQ115388583 ScholiaQ115388583MaRDI QIDQ2257999

Xingwang Xu, Quoc-Anh Ngô

Publication date: 2 March 2015

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00220-014-2133-7

zbMATH Keywords

positive smooth solutionEinstein-scalar field Lichnerowicz equations

Mathematics Subject Classification ID

Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Applications of PDEs on manifolds (58J90) Positive solutions to PDEs (35B09) Einstein equations (35Q76)

Related Items

The general relativistic constraint equations, On properties of positive solutions to nonlinear tri-harmonic and bi-harmonic equations with negative exponents, Lichnerowicz-type equations with sign-changing nonlinearities on complete manifolds with boundary, On the \(p\)-Laplacian Lichnerowicz equation on compact Riemannian manifolds, On the Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds, Prescribing Webster scalar curvature on CR manifolds of negative conformal invariants

Cites Work

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• Existence results for the Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds
• Stability and instability for Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds
• A variational analysis of Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds
• Conformal metrics with prescribed scalar curvature
• Scalar curvature and conformal deformation of Riemannian structure
• Problème de la courbure scalaire prescrite sur les variétés riemanniennes complètes. (The problem of prescribed scalar curvature for complete Riemannian manifolds)
• Stability and multiple solutions to Einstein-scalar field Lichnerowicz equation on manifolds
• Curvature functions for compact 2-manifolds
• Effective multiplicity for the Einstein-scalar field Lichnerowicz equation
• The Einstein-scalar field constraint system in the positive case
• Mathematical general relativity: A sampler
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• The constraint equations for the Einstein-scalar field system on compact manifolds
• Constant mean curvature solutions of the Einstein constraint equations on closed manifolds
• Courbures Scalaires Des Varietes D'Invariant Conforme Negatif
• The Lichnerowicz equation in the closed case of the Einstein-Maxwell theory